How do I find the maximum and minimum of a function in a given domain?

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Ria Singh
Ria Singh el 18 de Jul. de 2021
Comentada: Rik el 23 de Jul. de 2021
I'm trying to find the max and min of a function over a function, but I can't seem to figure out how. My equation is y = (1*x^4)/4+(4*x^3)/3- 5*(x^2)/2 over -3<=x<=3. I tried doing min(y) and max(y) but it's not working. Does anybody know how to find the max and min???
  2 comentarios
Image Analyst
Image Analyst el 23 de Jul. de 2021
Other than editing away most of your question, what else have you done? Did you like any of the Answers below?
Rik
Rik el 23 de Jul. de 2021
Original post (in case Ria decides to edit it away again):
How do I find the maximum and minimum of a function in a given domain?
I'm trying to find the max and min of a function over a function, but I can't seem to figure out how. My equation is y = (1*x^4)/4+(4*x^3)/3- 5*(x^2)/2 over -3<=x<=3. I tried doing min(y) and max(y) but it's not working. Does anybody know how to find the max and min???

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Respuestas (3)

Rik
Rik el 18 de Jul. de 2021
You need a function like fminbnd:
y =@(x) (1*x.^4)/4+(4*x.^3)/3- 5*(x.^2)/2;
x_min = fminbnd(y,-3,3)
x_min = -2.9999
Let's confirm this with a plot:
fplot(y,[-3 3])

Image Analyst
Image Analyst el 18 de Jul. de 2021
Try this:
x = linspace(-3, 3, 1000);
y = (1*x.^4)/4+(4*x.^3)/3- 5*(x.^2)/2;
plot(x, y, 'b-', 'LineWidth', 2);
grid on;
% Find where min is
[yMin, indexOfMin] = min(y);
fprintf('Min of y at x = %f, y = %f.\n', x(indexOfMin), min(y));
You get
Min of y at x = -3.000000, y = -38.250000.
Is that what you were looking for?

Walter Roberson
Walter Roberson el 19 de Jul. de 2021
syms x
y = (1*x.^4)/4+(4*x.^3)/3- 5*(x.^2)/2
y = 
LB = -3; UB = 3;
xcrit = solve(diff(y, x),x)
xcrit = 
xcrit(xcrit < LB | xcrit > UB) = [];
xcrit = unique([xcrit; LB; UB])
xcrit = 
ycrit = subs(y,x,xcrit)
ycrit = 
[miny, minidx] = min(ycrit)
miny = 
minidx = 1
[maxy, maxidx] = max(ycrit)
maxy = 
maxidx = 4
fprintf('minimum is %g at %g\n', miny, xcrit(minidx))
minimum is -38.25 at -3
fprintf('maximum is %g at %g\n', maxy, xcrit(maxidx))
maximum is 33.75 at 3

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